Applications Of Derivatives Question 177
Question: If a spherical balloon has a variable diameter $ 3x+\frac{9}{2} $ , then the rate of change of its volume with respect to x is
Options:
A) $ 27\pi {{(2x+3)}^{2}} $
B) $ \frac{27\pi }{16}{{(2x+3)}^{2}} $
C) $ \frac{27\pi }{8}{{(2x+3)}^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Radius of balloon = $ r=\frac{3}{4}(2x+3)\Rightarrow \frac{dr}{dx}=\frac{3}{2} $
$ \therefore $ Rate of change in volume = $ 4\pi {{( \frac{3}{4} )}^{2}}{{(2x+3)}^{2}}.\frac{3}{2} $
$ =\frac{27\pi }{8}{{(2x+3)}^{2}} $ .
BETA
